IDEAS home Printed from https://ideas.repec.org/a/hin/jnljam/524698.html
   My bibliography  Save this article

Geodesic B -Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds

Author

Listed:
  • Sheng-lan Chen
  • Nan-Jing Huang
  • Donal O'Regan

Abstract

We introduce a class of functions called geodesic -preinvex and geodesic -invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo -preinvex and geodesic quasi/pseudo -invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic -preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic -invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.

Suggested Citation

  • Sheng-lan Chen & Nan-Jing Huang & Donal O'Regan, 2014. "Geodesic B -Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, March.
    • Handle: RePEc:hin:jnljam:524698
    DOI: 10.1155/2014/524698
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JAM/2014/524698.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JAM/2014/524698.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/524698?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gabriel Ruiz-Garzón & Rafaela Osuna-Gómez & Antonio Rufián-Lizana & Beatriz Hernández-Jiménez, 2020. "Approximate Efficient Solutions of the Vector Optimization Problem on Hadamard Manifolds via Vector Variational Inequalities," Mathematics, MDPI, vol. 8(12), pages 1-19, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jnljam:524698. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.